We demonstrate a tunable cw terahertz (THz) parametric oscillator based on periodically poled MgO-doped lithium niobate, directly converting the 1030 nm pump wave into the THz regime. The tunability ranges from 1.2 to 2.9 THz at output power levels between 0.3 and 3.9 μW. To overcome the high pump threshold caused by THz absorption in the nonlinear crystal, we employ an enhancement cavity with a finesse of 500 at the pump wavelength. The intracavity pump threshold at 1.4 THz is measured to be 350 W for a crystal length of 2.5 cm.